---
date: 2022-04-18 11:58
modification date: Monday 18th April 2022 11:58:24
title: "scheme definitions"
aliases: [scheme definitions]
---

Last modified date: <%+ tp.file.last_modified_date() %>

---
- Tags: 
	- #study-guides 
- Refs:
	- Quick overview: <https://math.uchicago.edu/~may/REU2013/REUPapers/Fung.pdf#page=3>
- Links:
	- [scheme](scheme.md)

---

# scheme definitions


- [O_X module](Unsorted/O_X%20module.md)
	- [locally free sheaf](Unsorted/locally%20free%20sheaf.md)
- [ideal sheaf](ideal%20sheaf.md)
- [direct image](direct%20image.md)
- [inverse image](inverse%20image.md)
- [affine scheme](Unsorted/scheme.md)
- Common assumptions:
	- [Noetherian scheme](Noetherian%20scheme.md)
	- [integral scheme](integral%20scheme.md)
	- [separated scheme](separated%20scheme)
	- [regular in codimension one](Unsorted/regular%20scheme.md)
- [regular scheme](regular%20scheme.md)
- [Cohen-Macaulay](Unsorted/Cohen-Macaulay.md)
- [open subscheme](open%20subscheme.md)
- [closed immersion](Unsorted/closed%20immersion.md)
- [closed subscheme](Unsorted/closed%20immersion.md)
- [locally of finite type](Unsorted/finite%20type.md)
- [quasiseparated morphism](Unsorted/separated.md)
- [proper](Unsorted/proper%20morphism.md)
	- [universally closed morphism](universally%20closed%20morphism)
	- [separated morphism](Unsorted/separated.md)
	- [finite type](finite%20type.md)
- [projective (schemes)](Unsorted/projective%20(schemes).md)
- [quasiprojective scheme](Unsorted/projective%20(schemes).md)
- [flat morphism](flat%20morphism.md)
- [Proj](Proj)
- [sheaf associated to a module](sheaf%20associated%20to%20a%20module.md)
- [quasicoherent](Unsorted/quasicoherent%20sheaf.md)
- [invertible sheaf](Unsorted/invertible%20sheaves.md)
- [twisting sheaf](Unsorted/O(D)%20for%20D%20a%20divisor.md)
- [prime divisor](prime%20divisor)
- [Weil divisor](Weil%20divisor.md)